How can I make the camera taller in the Blender Game engine?
By making your camera taller do you mean to change the resolution? Your character and your camera should never be the same object. Make a cube (this will be your character), and parent the camera to it. The camera should be set to no collision and the box to dynamic. You can change the shape of the cube if you want the character to be taller. Or if you just want the camera to be higher up you could just move it up in the Z-axis.
If you are meaning resolution then you can simply adjust it in the Output tab under dimensions.